You guys spend a good chunk of Section 2.1 arguing that HAT-P-11’s magnetic activity is too low to explain the long-term RV signal, specifically to rebut the claims made by Basilicata et al. (2024). You calculate that using the older Noyes (1984) conversion gives a log R’HK of -4.79, which is “typical” and would require an impossibly steep RV-R’HK slope to explain the 60 m/s variation.
But then, in Section 3.2 and Table 1, you introduce an S-index correction in your RV modeling. The results show that including this correlation actually lowers the derived mass of planet c from 3.06 to 2.68 MJup. This is a huge red flag. If the activity is as negligible as you argue, why does including it change the planet’s mass by nearly 15%? It seems like the data is telling you that there is a meaningful correlation, which directly undermines the central premise you used to justify focusing on the planet hypothesis over the activity hypothesis. How can you justify using this correction while simultaneously arguing the star is too quiet for activity to matter? Isn’t this a fundamental inconsistency at the heart of your detection of planet c?
Your final, headline-grabbing result in Table 2 is that at 99% confidence, all vectors are misaligned to at least ~33°. But you only get this clean, tight constraint by combining the two possible inclination modes for planet c (prograde and retrograde). Looking at Figure 7, the story is much messier. If the star is edge-on (the favored case) and planet c is in the prograde mode, the obliquity peaks around 55° and 110°. If it’s in the retrograde mode, it peaks around 80° and 135°. These are very different physical configurations.
By mashing them together, you’re creating a posterior distribution that doesn’t actually represent any single physical reality. It’s like averaging a portrait of a cat and a dog and claiming you have a clear picture of an animal that is both. Given that the system’s future dynamical evolution (which you mention is in Paper II) depends critically on whether the orbit is prograde or retrograde, how can you justify combining these two distinct solutions into a single confidence interval? Aren’t you just erasing the very real degeneracy that remains in your data to make a stronger claim?